高加速度运动系统的非线性摩擦前馈补偿控制

高加速度运动系统中非线性摩擦的建模补偿对提高轨迹跟踪性能至关重要。本文针对传统参数化模型难以准确预估高加速度运动启停阶段摩擦过冲等非线性摩擦的问题,在传统模型结构的基础上,结合扩展Stribeck模型,提出一种扩展参数化模型,模型参数的训练和学习样本源于高精度迭代学习控制获取的有限轨迹下非线性摩擦前馈补偿数据,并采用Levenberg-Marquardt算法拟合模型参数。最后,在音圈电机驱动的高加速定位平台上针对不同运动轨迹进行了实验验证。结果表明,该方法能够克服传统参数化模型难以消除高加速度启停阶段摩擦过冲等非线性摩擦对轨迹跟踪精度的影响;且与迭代学习控制的轨迹跟踪精度接近,有效避免了迭代学习泛化性差等问题,可实现工作空间下任意轨迹的摩擦补偿。     

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

This paper presents a robust adaptive integral backstepping control strategy with friction compensation for realizing accurate and stable control of opto-electronic tracking system in the presence of nonlinear friction and external disturbance. With the help of integral control term to decrease the steady-state error of the system and combining robust adaptive control approach with the backstepping design method, a novel control method is constructed. Nonlinear modified LuGre observer is designed to estimate friction behavior. Robust adaptive integral backstepping control strategy is developed to compensate the changes in friction behavior and external disturbance of the servo system. The stability of the opto-electronic tracking system is proved by Lyapunov criterion. The performance of robust adaptive integral backstepping controller is verified by the opto-electronic tracking system with modified LuGre model in simulation and practical experiments. Compared to the adaptive integral backstepping sliding mode control method, the root mean square of angle error is reduced by 26.6% when the proposed control method is used. The experiment results demonstrate the effectiveness and robustness of the proposed strategy.     

基于预滑—动态摩擦力矩估计模型的自适应前馈补偿方法

根据数控交流伺服工作台进给系统从静止到宏观运动的过渡时间,和零速度时刻的指令加速度大小呈反比关系,区分摩擦力矩的预滑动区和滑动区,由此提出基于力矩值估计的摩擦补偿方法;在设定指令加速度后,基于命令力矩值的摩擦力矩模型,不需要测量速度就可以补偿工作台进给系统中的摩擦。同时,考虑到参数的不确定性,设计非线性摩擦自适应控制方案,对其稳定性进行理论证明。在交流伺服工作台进给系统上对基于摩擦力矩值估计的自适应前馈补偿方法进行验证。试验结果表明,基于预滑—动态摩擦力矩估计模型的自适应前馈补偿方法能实现在不同指令加速度下对期望轨迹的跟踪,并能大大提高系统的跟踪精度。     

飞机主动侧杆摩擦补偿研究

针对飞机主动侧杆系统中存在非线性摩擦因素,导致在飞机主动侧杆伺服系统中位置跟踪不精确,侧杆跟随性能下降的现象,在三环控制的基础上研究了Stribeck摩擦补偿方法。对Stribeck摩擦模型开展研究,并通过实验辨识其参数,将摩擦模型引入到飞机主动侧杆伺服系统中设计摩擦补偿方法,通过前馈补偿的方式在三环控制的基础上实现摩擦补偿。通过仿真和实验,对侧杆伺服系统摩擦补偿的可行性进行了验证。实验结果表明,所研究的摩擦补偿方法,提高了系统的稳态跟踪精度,具有较好的动态响应性能。     

Time-discretization of nonlinear systems with time delayed output via Taylor series

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, ‘hybrid’ discretization schemes resulting from a combination of the ‘scaling and squaring’ technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.     

含磁滞补偿的电液伺服系统预设性能跟踪控制

针对电液伺服系统普遍存在的参数不确定性、不确定非线性(磁滞、摩擦、外干扰等),提出一种基于自适应鲁棒控制的含磁滞补偿的预设性能跟踪控制策略。以阀控单出杆液压缸位置伺服系统为例,首先建立了含磁滞非线性的系统数学模型,然后通过定义预设性能函数,实现了对跟踪误差收敛速率、最大超调量和稳态精度的预先规划,基于规划后的转换误差设计了自适应鲁棒控制器,并提高了稳态和瞬态跟踪性能。仿真对比结果表明：该控制策略可以减小磁滞对系统跟踪精度的影响,提高跟踪误差的收敛速度,减小最大超调量,最终实现优良的跟踪性能。     

Fuzzy MRAC controller design for vane-type air motor systems

Air motors are widely used in the automation industry due to special requirements, such as spark-prohibited environments, the mining industry, chemical manufacturing plants, and so on. The purpose of this paper is to analyze the behavior of a vane-type air motor and to design a model reference adaptive control (MRAC) with a fuzzy friction compensation controller. It has been noted that the rotational speed of the air motor is closely related to the compressed air’s pressure and flow rate, and due to the compressibility of air and the friction in the mechanism, the overall system is actually nonlinear with dead-zone behavior. The performance of the previous controllers implemented on an air motor system demonstrated a large overshoot, slow response and significant fluctuation errors around the setting points. It is important to eliminate the dead-zone to improve the control performance. By considering the effects of the dead-zone behavior, we have developed an MRAC with fuzzy friction compensation controller to overcome the effect of the dead-zone. The following experimental results are given to validate the proposed speed control strategy.     

Test results of friction factor for round-hole roughness surfaces in closely spaced channel flow of water

For examining friction-factor characteristics of round-hole pattern surfaces which are usually applied on damper seals, flat plate test apparatus is designed and fabricated. The measurement method of leakage and pressure distribution along round-hole pattern specimen with different hole area is described and a method for determining the Fanning friction factor is discussed. Results show that the round-hole pattern surfaces provide a much larger friction factor than smooth surface, and the friction factor vs. clearance behavior yields that the friction factor generally decreases as the clearance increases unlike the results of Nava’s flat plate test. As the hole depth is decreased, the friction factor is increased, and maximum friction factor is obtained for 50% of hole area. Since the present experimental friction factor results show coincident characteristics with Moody’s friction factor model, empirical friction factors for round-hole pattern surfaces are obtained by using the Moody’s formula based on curve-fit of the experimental data. Results of Villasmil’s 2D CFD simulation support the present experimental test result.     

机载光电平台的复合补偿控制方法

为实现机载光电平台的实时高精度稳定跟踪控制,提出了一种基于改进干扰观测器和模糊逼近的复合自适应补偿控制方法.首先,根据系统的机械结构特点分析了各框架间的运动学耦合关系;考虑到载体扰动的影响,提出了一种基于速度信号的改进干扰观测器结构,并分析了它的工作原理和鲁棒稳定性.然后,针对机械系统中普遍存在的摩擦等干扰现象,设计了基于模糊逼近的复合补偿控制策略以保证系统的跟踪性能,最后,利用Lyapunov稳定性理论证明了系统的全局稳定性和跟踪误差的渐进收敛.实验结果显示,该控制方法具有较高的稳定精度,其跟踪误差可达μrad数量级,表明该方法可以有效地抑制载体扰动的影响并且具有良好的跟踪性能,是可行有效的.     

Adaptive robust motion trajectory tracking control of pneumatic cylinders with LuGre model-based friction compensation

Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation（RLSE） to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This paper constructs an adaptive robust controller     

基于LuGre模型的气动位置伺服系统摩擦补偿控制

气动伺服系统的摩擦力/驱动之比较大,摩擦力模型复杂、受影响因素较多且存在一定的不确定性,导致精确建模比较困难;另一方面,摩擦力和气体的低刚度、弱阻尼特性相互作用导致爬行、黏滑振荡现象,严重影响了伺服系统的动态及稳态性能的提升。在综合考虑摩擦力特征、系统自身非线性、未建模动态不确定性及摩擦力和系统性能相互影响的基础上,结合LuGre摩擦模型,采用双观测器估计摩擦力模型中的部分不确定性参数,提出非线性自适应反步摩擦补偿控制方法。通过在低速和高速工况下分别进行试验验证,并与PID控制方法进行比较,结果表明非线性自适应反步摩擦补偿控制方法有效改善了起步阶段的动态滞后现象,减少了低速工况下爬行及高速工况下的黏滑振荡现象,提高系统的响应速度及跟踪精度。     

Nonlinear supersonic flutter of truncated conical shells

A numerical model was developed to investigate the flutter instability of truncated conical shells subjected to supersonic flows. The exact solution of Sanders’ best firstorder approximation was used to develop the finite elements model of the shell. Nonlinear kinematics of Donnell’s, Sanders’ and Nemeth’s theories, in conjunction with the generalized coordinates method, were used to formulate the nonlinear strain energy of the shell. A pressure field was formulated using the piston theory with the correction term for the curvature. Lagrangian equations of motion based on Hamilton’s principle were obtained. A variation of the harmonic balance method was used for developing the amplitude equations of the shell, and a numerical method was used for solving these equations. Results of linear and nonlinear flutter of truncated conical shells were validated against the existing data in the literature. It was observed that geometrical nonlinearities have a softening effect on the stability of the shell in supersonic flows.     

Changes in Friction Properties of Monolayer Lubricant Films Induced by Development of Molecules’ Bonding

Functional perfluoropolyether (PFPE) films consisting of mobile and bonded molecules are widely used for lubrication of magnetic disks. In order to clarify the influence of film composition (mobile/bonded) on tribological performance, we measured the friction properties of two types of 2 nm-thick PFPE films (functional Zdol2000 and nonfunctional Z03) under lightly loaded (loading force: 0–1 mN) and quasi-static (low rotational speed: 2.1 mm/s) conditions as a function of elapsed time. The friction force of Z03 remained unchanged with time and increased linearly with loading force as described by Amontons’ law. In contrast, induced by the development of the molecules’ bonding in time, the friction force of Zdol2000 increased and transited to a nonlinear increase with loading force as time proceeded. The nonlinear friction-load relationship of Zdol2000 in the equilibrium state was characterized by the Johnson-Kendall-Roberts model.     

Nonlinear wave interaction of three Stokes’ waves in deep water: Banach fixed point method

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes’ waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes’ waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes’ waves’ interaction. The proposed method has a very fast convergence rate.     

新型摩擦模型的参数辨识及补偿实验研究

针对影响运动控制性能的非线性摩控因素,对一种新型摩擦模型的参数辨识及其基于摩控模型的补偿进行了实验研究,详细地给出了摩控模型参数的辨识步骤及补偿算法,实验结果表明,此辨识方案及补偿算法可以应用于工业的高精度运动控制中。     

随动系统的新型非奇异快速终端滑模控制

鉴于某舰载随动系统存在摩擦、海况等扰动因素,为提升系统控制精度及鲁棒性,提出了一种基于相位补偿的非奇异快速终端滑模控制(NFTSM+ARBF+TTD)方法.将泰勒公式与非线性函数fhan相结合,构造跟踪微分器,旨在减小相位延迟.在抑制微分过程噪声的基础上,应用泰勒公式进行相位补偿.设计自适应神经网络(ARBF)逼近扰动...     

液压振动台非线性摩擦力测量与参数辨识

电液伺服振动试验系统低速和换向时的非线性摩擦力测量和补偿是提高运输环境试验和地震模拟试验等控制精度的重要途径。为了定量获取液压振动台的非线性摩擦力,基于Stribeck效应建立了改进的电液伺服振动试验系统非线性摩擦力理论模型,并结合液压振动台的力平衡方程建立了非线性摩擦力待辨识参数的目标函数。提出一种基于位移闭环控制的简便方法对不同速度下的液压振动台油缸压力差进行测量,得到振动台液压缸与活塞杆之间的摩擦力随速度变化的数值规律。采用基于拟随机序列的混合遗传算法对非线性摩擦力理论模型的4个参数进行了辨识。试验结果证明了本研究方法的可行性,为液压振动试验系统加速度波形失真补偿提供了一定参考。     

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.     

Control system design of a linear motor feed drive system using virtual friction

This paper proposes a friction compensator and a design method for control systems to improve the response characteristics of linear motor feed drive systems. The proposed friction compensator cancels the real nonlinear friction of feed drive systems by using the nonlinear friction model proposed in this study and introduces virtual linear friction to facilitate the control system design. The proposed design method enables the determination of servo gains and friction compensator parameters that lead to desirable tracking performance and disturbance rejection without many trial-and-error tuning processes. In addition, the proposed method facilitates the design of the velocity feedforward compensator by using the inverse transfer function of the velocity control loop to correct the position tracking errors for various position commands. The effectiveness of the proposed method with the friction compensator and the velocity feedforward compensator was verified in simulations and experiments using a one-axis feed drive system consisting of a rod-type linear motor and linear roller guides. The results confirmed that the proposed method enables desirable overshoot-free responses and corrects motion trajectory errors due to nonlinear friction characteristics, and the proposed velocity feedforward compensator can correct tracking errors in both constant velocity motion and circular motion.     

Robust nonlinear control of a 6 DOF parallel manipulator : Task space approach

This paper presents a robust nonlinear controller for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The proposed control strategy requires information on orientations and translations in the task space unlike the joint space or link space control scheme. Although a 6 DOF sensor may provide such information in a straightforward manner, its cost calls for a more economical alternative. A novel indirect method based on the readily available length information engages as a potential candidate to replace a 6 DOF sensor. The indirect approach generates the necessary information by solving the forward kinematics and subsequently applying alpha-beta-gamma tracker. With the 6 DOF signals available, a robust nonlinear task space control (RNTC) scheme is proposed based on the Lyapunov redesign method, whose stability is rigorously proved. The performance of the proposed RNTC with the new estimation scheme is evaluated via experiments. First, the results of the estimator are compared with the rate-gyro signals, which indicates excellent agreement. Then, the RNTC with on-line estimated 6 DOF data is shown to achieve excellent control performance to sinusoidal inputs, which is superior to those of a commonly used proportional-plus-integral-plus-derivative controller with a feedforward friction compensation under joint space coordinates and the nonlinear controller under task space coordinates.